01242nas a2200121 4500008004100000245005600041210005400097260001000151520082800161653007700989100001801066856003601084 2013 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA3 aWe study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce a topology for the cracks suitable to remove the restrictions on the regularity of the crack set and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity at each of its points. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith\\\'s theory, in terms of the energy release rate, when the crack grows at least at one point of its front.10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttp://hdl.handle.net/1963/6490